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Two Parallel Currents

A charge Q1 i...

Question

A charge $Q_{1}$ is placed at $O$ inside a hollow conducting sphere having inner and outer radii as $10 m$ and $11 m$ as shown in the figure. The force experienced by $Q_{2}$ at $P$ is $F_{1}$ when $Q_{1}$ is placed at the center and force experienced by $Q_{2}$ when $Q_{1}$ is placed at $O$ is $F_{2}$ . Then $\frac{F_{1}}{F_{2}}$ is equal to

A

1

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B

{(\frac{12}{13})}^{2}

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C

{(\frac{13}{12})}^{2}

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D

None of the above

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E

1

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F

{(\frac{12}{13})}^{2}

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G

{(\frac{13}{12})}^{2}

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H

None of the above

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Solution

The correct option is A $1$
Given,

Inner radius of hollow conducting sphere $r_{1} = 10 m$

Outer radius of hollow conducting sphere $r_{2} = 11 m$

From the given figure, it is clear that, the force on charge $Q_{2}$ is due to induced charge on outer surface of hollow sphere which does not depend upon the location of charge $Q_{1}$ .

So, we can conclude that, $F_{1} = F_{2} \Rightarrow \frac{F_{1}}{F_{2}} = 1$

Hence, option (a) is the correct answer.

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Two Parallel Currents

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